AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs

TL;DR

The paper introduces the AZ-whiteness test, a novel statistical method for detecting serial and spatial dependencies in multivariate time series on dynamic graphs, applicable to various real-world networked systems.

Contribution

It presents the first whiteness test for graph signals that accounts for dynamic, weighted, and changing graph topologies, extending traditional methods to complex spatio-temporal data.

Findings

The AZ-test effectively detects dependencies in synthetic and real-world data.

It can assess the quality of spatio-temporal forecasting models.

The test's asymptotic distribution is known without assuming identical data distribution.

Abstract

We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.